Bayesian Value-at-Risk for a Portfolio: Multi- and Univariate Approaches Using MSF-SBEKK Models

Jacek Osiewalski and Anna Pajor

Central European Journal of Economic Modelling and Econometrics, 2010, vol. 2, issue 4, 253-277

Abstract: The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.

Keywords: Bayesian econometrics; risk analysis; multivariate GARCH processes; multivariate SV processes; hybrid SV-GARCH models (search for similar items in EconPapers)
JEL-codes: C11 C22 C32 C53 G17 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (7)

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